Design of Stable Concave Slopes for Reduced Sediment Delivery during Geomorphic Reclamation

This paper is a synthesis of previous published works that have arisen out of an investigation of the stability and sediment control considerations in reclaimed mine lands. Methods currently exist to estimate both the mechanical slope stability of the slopes and the hillslope sediment delivery. However, these methods require input parameters that are obtained from laboratory or field measurements, or through empirical relationships, many of which were not developed for mine lands. Further, these methods have been developed for slopes that are planar in cross section or profile, and existing studies would suggest concave slopes may reduce surface erosion and sediment. This synthesis addresses the following: a) soil characterization and mechanical stability of steep reclaimed slopes with a low compaction surface layer, b) hydrology curve number and revised universal soil loss equation (RUSLE) erodibility (K) factor for Appalachian surface coal mining reclamation sites, c) testing of the SEDCAD model performance for applicability for steep-sloped reclaimed mine lands, and d) superior mechanical stability and erosional resistance of concave slopes relative to planar slopes.


 Problem Statement
 Methods exist to estimate: 1) mechanical slope stability, and 2) hillslope sediment delivery  However, methods have been developed for planar slopes, and existing studies would suggest concave slopes may improve stability coupled with reductions in surface erosion.
 In this presentation we:  Summarize field experiments quantifying the Revised Universal Soil Loss Equation (RUSLE) erodibility (K) factor for Appalachian surface coal mining reclamation sites.
 Demonstrate that concave slopes may provide improved performance than planar slopes in terms of both mechanical and erosional resistances.
 Demonstrate that RUSLE2 model is suitable for estimating sediment yields from reclaimed soil materials and slopes with concave geometries.Concave-linear slope generated less sediment than other slope types: 14.9 kg per 1031 liters runoff.

Background
 Concave slopes appear to be the result of long-term fluvial geomorphological processes leading to equilibrium conditions in slopes. The growth of precision auto-guidance construction equipment allows complex shapes to be built with high level of precision. The following approximate solution for the problem of the slope at a critical state was developed (Jeldes et al., 2014) 18 Proposed Solution for the Critical Slope ( )  Verification of the FS for the obtained concave slope via Finite Element analyses (same obtained via Limit Equilibrium)   Results shown in terms of shear strains for the example problem with strength reduced SRF=1.52 to emphasize failure mode.(Assumed υ=0.3, E=20,000 kPa. )

Illustrative Example
 Slopes in nature are seldom planar in cross section.
 Concave slopes generally require less reclaimed material than planar slopes with same FS.
 Concave slope profiles produce less sediment.
 An approximate analytical solution was proposed yielding the coordinates of a concave slope at critical equilibrium or imminent failure.Concave slopes can be obtained for any FS.
 Results from RUSLE2 analyses indicate that the concave slopes proposed here yield 15-40% less sediment than planar slopes of equal FS, regardless of soil erodibility and weather conditions.
 Results from the sensitivity analyses reveal that the stability of concave slopes is not significantly influenced by errors in the constructed profile of as great as 200 mm of vertical deviation.

Background 4 
Land-forming Geomorphic Reclamation approaches  Can include the construction of concave shapes in the transversal and longitudinal (down-slope) directions  More natural features with improved stability and erosion resistance Transversely concave Longitudinally concave (concave profile) Anaheim Hills (Schor and Gray 2007)  Gravitational stresses in slopes increase with depth  To maintain a uniform Factor of Safety (FS) the inclination must decrease downslope  Erosional stresses on the surface of the slope increases with inclination and distance  If the slope inclination decreases as we move downslope, the erosional stresses are more uniform and lower  For these reasons, slopes observed in nature are usually not planar Background (Adapted from Schor and Gray 2007) Background  Concave slopes lead to less erosion than planar slopes Rieke-Zapp and Nearing (2005): Experimental study -3D slope shape vs erosional resistance.

Background
Slopes obtain concave equilibrium after parallel retreat of the slope with spatial occurrences of erosion and deposition (Nash 1980; Twidale 2007; Pelletier and Rasmussen 2009) Background Mountainside Coal Mine Reclaimed Slope, Claiborne TN National Coal Mine Reclaimed Slope, Campbell TN Current reclamation sites in the Appalachian: planar man-made slopes.Lessons from Australia (Howard et al. 2011)  Concave profiles for reduced sediment delivery on mine reclaimed slopes.It is possible to built concave slopes! Replication of observed concave profiles without quantitative design can be an unpredictable practice with engineering risk.

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Background www.landloch.com.au/technical-notes/11NOT all concave profiles may be mechanically stable; therefore  What is the optimum concave profile for stability considerations?Supporting Research on Erosion 12Hoomehr et al. (2013Hoomehr et al. ( , 2014) ) measured runoff and sediment yield from three coal mining sites in East Tennessee in order to provide accurate input parameters for the SEDCAD model. Computed a hydrology Curve Number (CN) and RUSLE erodibility K factor. Measured runoff and sediment by an unique study design using Pinson et al. (2009) collection devices.Hoomehr and Schwartz (2013) Supporting Research on Erosion 13  Hydrology Curve Number for steep-sloped reclaimed mine sites determined to be: CN = 59  RUSLE: A = R .K .LS .C .P  A = Amount of soil loss  R = Rainfall erosivilty  K = Soil erodibility  LS = Combined length-slope factor  C = cover management factor  P = erosion control management factor  Measured A from collected sediment, measured R from rainfall data, measured LS from field surveys of study plots, assumed C and P = 1.Therefore, K computed per:  K = A/(R .LS)  Results of K computations ranged from 0.001 to 0.05 t.ha.h/(ha.MJ.mm)  High K factors occurred during rill development, followed my slope erosional stabilty.Hoomehr et al. (2013, 2014) Supporting Research on Erosion 15 SEDCAD modeling performance tended to overestimate sediment yields up to 1.6 times greater than measured, however results were variable.SEDCAD model was sensitive to selection of CN, for example a 40 % deviation in selection would approximately double sediment yields from the model.Develop a design methodology for concave slopes with a selected degree of stability or design Factor of Safety (FS) Investigate the difference in soil loss (surficial erosion) between concave and planar slopes that satisfy the same degree of mechanical stability  Investigate the precision to which concave forms can be constructed, and how this affects the desired slope stability 16Concave Slope Design Objectives  Plasticity theory:Sokolovskiĭ (1960Sokolovskiĭ ( , 1965)   )     Equations of the characteristics that describe slip lines where the plastic deformation occurs in the soil

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Key: use a strength reduction factor equal to the desired factor of safety to obtain: The designer can select the performing Factor of Safety.Sediment yield (A) determined from the widely used RUSLE2 for concave and planar slopes with same FS  A wide range of soil erodibility values were investigated, including those typically observed in mine reclamation(Hoomehr et al. 2014).Example results for a silt soil.21 RUSLE2 Erosion Analyses Concave slopes yielded less sediment than equally stable planar slopes for all the erodibility values and slope heights investigated For the range of values investigated, ranges from 0.85 -0.60 , indicating that concave slopes yield 15 -40% less sediment than their planar counterparts For TN sites RUSLE K factor = 0.001 -0.05 t.ha.h/(ha.MJ.mm) ); Hoomehr et al. (2014)  Vertical accuracy of 3D grade control systems is commonly within 30 mm (horizontal accuracy in the millimeter scale)  We investigated a vertical accuracy T = 200 mm, which may be also achieved by conventional equipment  FS's are not significantly influenced by improper construction within the 200 mm of vertical accuracy 22 Sensitivity to Construction  The worst case scenario: the vertical component of the contour is constructed deeper than designed, resulting in